No way Mammal!

A girl, learning about Mongolia, coming across a fact about the “Horse People” drinking horse milk.
Girl: “No way! Horses don’t have milk!”
Me: “Actually, they do. They are mammals, and all mammals have milk for their young.”
Girl (eyeing me suspiciously): “Na-ah, only cows and goats have milk.”
Me: “The milk that we drink and use indeed comes from cows and goats and sheep, but all mammals have milk for their babies. Including horses.”
The girl, incredulous and rather alarmed. “No way! You are just saying this to trick me”
Me: “Nope. Not tricking you.”
Girl:”Yes you are, only cows have milk. And goats and stuff. Not horses. What are you going to say next, that zebras have milk, too?”
Me (smiling): “Yep, they do. And lions, and hippos, and giraffes, and mice…”
Girl (adamant): “Stop it! Mice are way to small to be mammals…”

And so it went. On whales, and elephants, bats and rabbits, gorillas and dogs (“No way!”)
She demanded an internet search to prove I was not pulling her leg but then refused to believe that, either.

We went back to animal groupings. Bird, Reptiles, Mammals…

After a while of this, glee rose in her eyes. She was sure she finally found the loophole to absolutely prove me wrong.
“So,” she said, victorious, “if you say that mammals have hair or fur and have teeth and have live babies and all that, then I KNOW you are wrong because then you’d have to tell me that we’re mammals, too!”